(\partial)/(\partial x)(2x^2-4xy+y^4)

Lösung

\frac{\partial}{\partial x} (2 x^{2} - 4 x y + y^{4})

4 x - 4 y

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x^{2} - 4 x y + y^{4})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (2 x^{2}) - \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (y^{4})

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

\frac{\partial}{\partial x} (4 x y) = 4 y

\frac{\partial}{\partial x} (y^{4}) = 0

= 4 x - 4 y + 0

Vereinfache

= 4 x - 4 y

\frac{d}{d x} (2 x - x + 3)

d er i v a t i v e sin^{2} (x^{2})

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = 0

y^{^{'}} = - 3 y + e^{- 2 x}

\int_{- 1}^{1} x^{2} + 1 d x